AM1* parameters for cobalt and nickel

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Hakan Kayi, Timothy Clark

To cite this version:

Hakan Kayi, Timothy Clark. AM1* parameters for cobalt and nickel. Journal of Molecular Modeling, Springer Verlag (Germany), 2009, 16 (1), pp.29-47. �10.1007/s00894-009-0503-4�. �hal-00568326�

Manuscript Number: JMMO735R1

Title: AM1* parameters for cobalt and nickel Article Type: Original paper

Keywords: AM1*; Cobalt parameters; Nickel parameters; Semiempirical MO-theory Corresponding Author: Prof. Tim Clark,

Corresponding Author's Institution: Universitaet Erlangen-Nurnberg First Author: Hakan Kayi

Order of Authors: Hakan Kayi; Tim Clark

Abstract: We report the parameterization of AM1* for the elements Co and Ni. The basis sets for both metals contain one set each of s-, p- and d orbitals. AM1* parameters are now available for H, C, N, O and F (which use the original AM1 parameters), Al, Si, P, S, Cl, Ti, V, Cr, Co, Ni, Cu, Zn, Br, Zr, Mo and I.

The performance and typical errors of AM1* are discussed for Co and Ni and compared with available NDDO Hamiltonians.

Response to Reviewers: Dear Andrzej,

we have revised our manuscript in accord with the referees’ comments as follows:

Reviewer 1:

1. “Phtalocyanine” has been corrected throughout 2. “Co#P” has been corrected to CoP

3. nickel dimethylglyoxime is now mentioned by name

4. The error for CoTi has been reduced to zero, but this cannot be done for CoZr. This is because the two variables are not independent (i.e. there is not necessarily a combination of the two that gives zero errors in Heat of Formation and Bond length)

I trust the paper will now be acceptable for publication.

Best wishes Tim

1

AM1* parameters for cobalt and nickel

Received: 20.02.2009 / Accepted: 17.04.2009

Hakan Kayi and Timothy Clark



Email: clark@chemie.uni-erlangen.de

Computer-Chemie-Centrum and Interdisciplinary Center for Molecular Materials, Friedrich-Alexander-Universität Erlangen-Nürnberg, Nägelsbachstraße 25, 91052 Erlangen, Germany

Abstract

We report the parameterization of AM1* for the elements Co and Ni. The basis sets for both metals contain one set each of

and d-orbitals. AM1* parameters are now available for H, C, N, O and F (which use the original AM1 parameters), Al, Si, P, S, Cl, Ti, V, Cr, Co, Ni, Cu, Zn, Br, Zr, Mo and I. The performance and typical errors of AM1* are discussed for Co and Ni and compared with available NDDO Hamiltonians.

Keywords

AM1*  Cobalt parameters  Nickel parameters  Semiempirical MO-theory

Introduction

AM1* [1-5] is an extension of AM1 [6] that uses d-orbitals for the elements P, S, Cl, [1] Al, Si, Ti and Zr, [2] Cu and Zn, [3] Br and I, [4] V and Cr [5]. The AM1* molybdenum parameters are a slight modification of Voityuk and Rösch’s AM1(d) parameter set [7].

AM1* retains the original AM1 parameters for the elements H, C, N, O and F. The intention is to provide a technique that has the advantages of AM1 for first-row elements, such as good energies for hydrogen bonds, higher rotation barriers for

PM3 [10-12] but performs better for heavier elements and to be applicable to the first row transition metals. As a continuation of this work, we now report AM1* parameters for cobalt and nickel. Both cobalt and nickel are important in the chemistry of organometallic and biological catalysts [13, 14]. Because the experimental data for heats of formation of compounds of these two metals are relatively sparse, we have also used a series of model compounds whose heats of formation we have derived from DFT calculations [15].

Theory

AM1* for the two new elements uses the same basic theory as outlined previously [1, 2]. As for other element-H interactions, the core-core repulsion potential for the Co-H and Ni-H interactions used a distance-dependent term

, rather than the constant term used for core-core potentials for most other interactions in AM1* [1]. This distance-dependent

was also used for the Mo-H and interaction in AM1(d) [7] and for Ti-H, V-H, Cr-H, Cu-H, Zn-H, Br-H, Zr-H, Mo-H and I-H in AM1* [2-5]. The core-core terms for Co-H and Ni-H are thus:

 

( )

1 exp

core

i j ss ij ij ij ij

E i  j  Z Z  ^   r    r ^  ⁽¹⁾

where all terms have the same meaning as given in reference [1].

The standard MNDO/d formula is used for all other core-core interactions:

 

( )

1 exp

core

i j ss ij ij ij

E i  j  Z Z  ^      r ^  ⁽²⁾

The parameterization techniques were those reported in references [1] and [2] and will not be described further here.

Parameterization data

The target values used for parameterization and their sources are defined in Table S1 of the Supplementary Material. We have used both reaction energies and heats of formation as we did for the Ti, Zr, Cu, Zn, Br, I, V and Cr parameterizations [2-5] and have also used a small series of model compounds whose heats of formation we have derived from DFT calculations.

As before, [1-5] we checked that experimental values for heats of formation were reasonable using DFT calculations.

DFT calculations used the Gaussian 03 suite of programs [16] with the LANL2DZ basis set and standard effective core potentials [17-20] augmented by a set of polarization functions [21] (designated LANL2DZ+pol) and the B3LYP hybrid functional [22-24].

Experimental parameterization data for cobalt and nickel were taken largely from the NIST Webbook, [25] but also from the OpenMopac collection [26] and the other experimental and theoretical sources given in the Supplementary Material.

The energetic parameterization data and their sources are given in Table S1 of the

Supplementary Material. In addition to the energetic data, geometries, dipole moments and

ionization potentials taken from the above sources, crystal structures from the Cambridge

Structural Database (CSD) [27] were used in the parameterization to ensure that not only the

energetic and electronic properties for the “prototype” compounds, but also the structures of

large cobalt and nickel compounds are well produced.

Results

The optimized AM1* parameters are shown in Table 1. Geometries were optimized with the new AM1* parameterization using VAMP 10.0, [28] while the PM5 calculations used LinMOPAC2.0 [29] and those with PM6 used MOPAC2007 [30]. The three programs give essentially identical results for the Hamiltonians that are available in all three.

- Table 1 about here -

Cobalt

Heats of formation

The calculated heats of formation for our training set of cobalt compounds are shown in Table 2. We have compared our results with Stewart’s recently published PM6 method [31]

and also unpublished PM5 method implemented in LinMopac [29].

- Table 2 about here -

AM1* reproduces the heats of formation of the training set of cobalt compounds used in parameterization better than either PM6 or PM5. The mean unsigned error (MUE) for the AM1* parameterization dataset is 20.5 kcal mol

, compared with 61.9 and 84.3 kcal mol

for PM6 and PM5, respectively. PM6 produces large errors for the compounds that were not included in its original training set. The parameterization data set for PM5 has not been published, but clearly does not cover the range of compounds used for AM1*. All three methods tend to underestimate heats of formation to cobalt-containing compounds. However, this tendency is less pronounced for AM1* (mean signed error (MSE) -7.4 kcal mol

) than PM6 and PM5 (MSEs of -48.6 and -70.8 kcal mol

, respectively).

The largest single positive error for AM1* is found for Co

(108.4 kcal mol

). This is potentially disturbing as the ionization potential of Co is an important determinant of the reactivity of cobalt centers. However, we cannot detect serious systematic trends caused by this error. Molecules that give the largest positive errors are C

H

NS

CoI (GECVEP) (52.0 kcal mol

), CoC

N

H

O

(AMGXCO01) (39.3 kcal mol

) and CoCl

(33.8 kcal mol

). The largest negative errors are found for Co(H

O)

(-110.0 kcal mol

), CoO

(-75.5 kcal mol

),

CoOBr (-68.6 kcal mol

) and HCoPH

(-53.2 kcal mol

). The large negative errors with oxygen-containing compounds are not surprising as we have pointed out in our previous parameterizations [5]. AM1* uses the unchanged AM1 parameterization for the elements H, C, N, O and F, which limits the possible accuracy of the parameterization. In this respect, the heats of formation of Co(H

O)

and Co(H

O)

agree remarkably well with experiment considering the large AM1* errors for Co

and Co

(see below). As found for other metals, the large errors in pure AM1* element-containing compounds is likely to be a consequence of our sequential parameterization strategy, in contrast to the simultaneous parameterization used for PM6 [31].

Not only AM1* gives very large errors for cobalt di-, tri-, tetra- and penta-cations (not shown in Table 2 and not included in the statistics), but also PM6 and PM5. AM1* errors are found to be 143.0 kcal mol

(-96.5 and 119.6 kcal mol

for PM6 and PM5, respectively) for Co

, 131.8 kcal mol

(-545.6 and -126.7 kcal mol

for PM6 and PM5, respectively) for Co

, - 56.8 kcal mol

(-1356.1 and -335.6 kcal mol

for PM6 and PM5, respectively) for Co

and - 704.5 kcal mol

(-2758.8 and -902.8 kcal mol

for PM6 and PM5, respectively) for Co

. Experimental heats of formation of these cations are given in Table S1 of the Supplementary Material. Nonetheless, on aggregate AM1* performs better than the other available methods for the heats of formation of cobalt compounds.

Table 2, however, also shows the performance of the three methods for only the PM6 parameterization dataset [31]. These data demonstrate the influence of the extent of the training data. AM1* performs approximately equally well for its own training set and for the subset used to parameterize PM6, whereas PM6 performs significantly better for the subset for which it was trained. This situation is unavoidable and is a direct consequence of the relative paucity of data for parameterizing semiempirical MO techniques for transition metals.

Ionization potentials and dipole moments

A comparison of the calculated and experimental Koopmans’ theorem ionization potentials and dipole moments for AM1*, PM6 and PM5 are shown in Table 3.

- Table 3 about here -

The performance of the three methods is comparable. The mean unsigned errors vary in a relatively small range from 0.99 (PM5) to 1.50 eV (PM6). The AM1* MUE, 1.23 eV, lies in the middle of this range. With an MSE of -0.16 eV, AM1* tends to underestimate ionization potentials slightly, whereas PM6 and PM5 overestimate them by 0.80 and 0.41 eV, respectively.

Large AM1* errors are found for CoCl

(-2.10 eV), CoCH

(1.88 eV), CoC

H

(1.87 eV) and Co(CO)

(-1.54 eV). The large error for CoCl

may originate from a general weakness in the original chlorine parameterization, whereas the others may be an indirect result of using the original AM1 parameters for hydrogen, carbon and oxygen.

AM1* and PM5 show positive systematic errors for the dipole moments of cobalt compounds, whereas PM6 with 0.03 Debye (MSE) shows no tendency to systematic errors. AM1* and PM5 overestimate dipole moments by 0.34 and 1.13 Debye (MSE), respectively. AM1*

performs well, with an MUE of 0.69 Debye for the dipole moments of the training set of cobalt compounds. The largest AM1* errors are found for CoI (2.76 Debye) and CoBr (-1.77 Debye). These errors may be a consequence of our sequential parameterization strategy. The MUEs for PM6 and PM5 are found to be 1.03 and 1.76 Debye, respectively.

Geometries

Table 4 shows a comparison of AM1*, PM6 and PM5 results in reproducing the geometries of the cobalt-containing compounds.

- Table 4 about here -

AM1* and PM5 overestimate bond lengths to cobalt-containing compounds systematically by

0.04 and 0.36 Å, respectively, whereas PM6 underestimates them by 0.03 Å. AM1*, with an

MUE of 0.08 Å performs quite well for bond lengths, compared with MUEs of 0.16 Å and

0.51 Å for PM6 and PM5, respectively. On the other hand, PM6 (MUE=7.1°) performs

slightly better than AM1* (MUE=9.3°) and far better than PM5 (MUE=16.7°) for the bond

angles. In general, AM1* gives bond angles for cobalt-containing that are on average 1.5° too

small, whereas PM6 and PM5 give bond angles are too large by 4.0° and 5.1°, respectively.

Nickel

Heats of formation

The results obtained for heats of formation of nickel-containing compounds are shown in Table 5.

- Table 5 about here -

Table 5 shows that, for the training set used, AM1* reproduces heats of formation of nickel- containing compounds slightly better than PM6 and far better than PM5. The mean unsigned error between target and AM1*-calculated heats of formation is 21.5 kcal mol

. For PM6 and PM5, the MUEs are found 27.3 and 53.0 kcal mol

, respectively. AM1* and PM6 underestimate heats of formation to nickel compounds by 6.7 and 4.3 kcal mol

, respectively (MSEs). PM5 systematically predicts heats of formation to be too positive with a mean signed error of 21.0 kcal mol

. The largest positive errors for AM1* are found for the compounds NiC

N

H

S

O

(53.6 kcal mol

), Ni(H

S)

(53.1 kcal mol

), NiH

(50.6 kcal mol

), NiCO (48.0 kcal mol

) and nickel dimethylglyoxime (NiC

N

H

O

, NIMGLO01) (42.0 kcal mol

). The largest negative errors for AM1* are found for Ni(CN)

(-108.4 kcal mol

), NiC

N

S

(CUSJUV) (-79.1 kcal mol

), Ni(CN)

(-73.7 kcal mol

). AM1* also gives negative errors for the chlorinated compounds NiCH

Cl, NiCl

O, cis- and trans-NiCl

.(H

O)

and

)

S)

Cl

more than 30 kcal mol

. Large errors in AM1* are given by the compounds that contain original AM1 elements or AM1 elements with sulfur, and also from the chlorinated compounds. We attribute this to a weakness in the AM1*

parameterization for the chlorine and the sulfur, and also general weakness of the original AM1 parameterization.

Once again, Table 5 shows the results obtained with the three methods for the PM6 training

set [31]. AM1* systematically gives heats of formation that are too negative (MSE = -12 kcal

mol

), but otherwise performs similarly for the PM6 subset and the complete dataset. PM6

clearly gives some additional outliers with the AM1* training set that decrease its statistical

performance a little, whereas PM5 actually performs slightly better for the AM1* dataset than

for the PM6 subset (but worse than the other two methods).

Ionization potentials and dipole moments

A comparison of the calculated and experimental Koopmans’ theorem ionization potentials and dipole moments for the compounds containing nickel are shown in Table 6.

- Table 6 about here -

AM1* shows no systematic error-trend in the reproduction of Koopmans’ theorem ionization potentials of nickel-containing compounds for the dataset used. PM6 underestimates ionization potentials to nickel compounds by 1.09 eV, whereas PM5 overestimates them by 0.73 eV. AM1* performs slightly better than PM6 (MUE=1.43 eV) and PM5 (1.83 eV) with an MUE of 1.17 eV.

The performance of the three methods is comparable for dipole moments. The mean unsigned errors vary in a narrow range from 1.73 (PM6) to 1.89 Debye (AM1*). The PM5 MUE is found to be 1.82 Debye. All three methods systematically underestimate dipole moments of nickel compounds. Mean signed errors are found to be -0.52, -0.82 and –0.89 Debye for PM5, AM1* and PM6, respectively. All the large AM1* errors are found for the compounds either contain original AM1 elements or chlorine.

Geometries

The geometrical parameters used to parameterize AM1* for nickel and a comparison of the AM1*, PM6 and PM5 results are shown in Table 7.

- Table 7 about here -

AM1* with a mean unsigned error of 0.09 Å performs slightly better than PM6 (MUE=0.11 Å) and far better than PM5 (MUE=0.33 Å) for bond lengths to nickel compounds. PM6 (MSE=0.01 Å) and AM1* (MSE=0.04 Å) show no significant systematic trend, whereas PM5 (MSE=0.24) seriously overestimates bond lengths to nickel.

The performance of AM1* for bond angles to nickel compounds is comparable to PM6 and

better than PM5. The MUEs for AM1* and PM6 are 10.2° and 10.7°, respectively, and for

PM5 15.9°. AM1* shows no significant systematic error with an MSE of 0.2°, whereas PM6

(MSE=-5.1°) and PM5 (MSE=-4.6°) predict the bond angles to be too small.

Discussion

Our new AM1* parameters for cobalt and nickel provide important additional elements especially for catalytic chemistry applications based on organometallic compounds of the two metals. As for our previous parameterizations, we have extended the range of the parameterization dataset and made it more reliable by including results from DFT calculations. For the training set used, AM1* parameterizations for cobalt and nickel give good energetic and electronic results. Additionally, AM1* performs very well for the structural properties.

As published NDDO-based semiempirical molecular orbital techniques that use

both AM1* and PM6 have very similar theoretical frameworks and provide a good opportunity to carry out comparative calculations for many different applications and provide good starting points for the reaction-specific local parameterizations. As for all semiempirical methods, AM1* and PM6 are likely to give large errors that were not revealed during parameterization. This is illustrated well by comparing their performance for the dataset used to parameterize PM6. The additional compounds in the AM1* dataset give slightly larger errors with PM6. The availability of two independently parameterized techniques of similar quality should, however, provide an additional validation possibility for semiempirical MO calculations on transition metal species.

Acknowledgments

This work was supported by the Deutsche Forschungsgemeinschaft by an individual grant (Cl85/17-1) and as part of GK312 “Homogeneous and Heterogeneous Electron Transfer” and SFB583 “Redox-Active Metal Complexes: Control of Reactivity via Molecular Architecture”.

We thank Dr. Paul Winget, Dr. Bodo Martin, Dr. Cenk Selcuki, Dr. Matthias Hennemann and

Anselm Horn for support with the parameterization database.

Supplementary material

The values and the sources of the parameterization data.

References

1. Winget P, Horn AHC, Selçuki C, Martin B, Clark T (2003) J Mol Model 9:408-414 2. Winget P, Clark T (2005) J Mol Model 11:439−456

3. Kayi H, Clark T (2007) J Mol Model 13:965-979 4. Kayi H, Clark T (2009) J Mol Model 15:295-308 5. Kayi H, Clark T (2009) J Mol Model 15 (in the press)

6. Dewar MJS, Zoebisch EG, Healy EF, Stewart JJP (1985) J Am Chem Soc 107:3902-3909 7. Voityuk AA, Rösch N (2000) J Phys Chem A 104:4089-4094

8. Dewar MJS, Thiel W (1977) J Am Chem Soc 99:4899-4907

9. Thiel W (1998) In: Schleyer PvR, Allinger NL, Clark T, Gasteiger J, Kollman PA, Schaefer III HF, Schreiner PR (eds) Encyclopedia of Computational Chemistry. Wiley:

Chichester, p 1599

10. Stewart JJP (1989) J Comp Chem 10:209-220 11. Stewart JJP (1989) J Comp Chem 10:221-264

12. Stewart JJP (1998), In: Schleyer PvR, Allinger NL, Clark T, Gasteiger J, Kollman PA, Schaefer III HF, Schreiner PR (eds) Encyclopedia of Computational Chemistry. Wiley:

Chichester, p 2080

13. Shubina TE, Marbach H, Flechtner K, Kretschmann A, Jux N, Buchner F, Steinrück HP, Clark T, Gottfried JM (2007) J Am Chem Soc 129:9476-9483

14. Bennett BL, Shannon White S, Brittany Hodges B, Dane Rodgers D, Ade Lau A, Roddick DM (2003) J Organomet Chem 679:65-71

15. Winget P, Clark T (2004) J Comp Chem 25:725-733

16. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR,

Montgomery JA Jr, Vreven T, Kudin KN, Burant JC, Millam JM, Iyengar SS, Tomasi J,

Barone V, Mennucci B, Cossi M, Scalmani G, Rega N, Petersson GA, Nakatsuji H, Hada

M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao

O, Nakai H, Klene M, Li X, Knox JE, Hratchian HP, Cross JB, Bakken V, Adamo C,

Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C,

Ochterski JW, Ayala PY, Morokuma K, Voth GA, Salvador P, Dannenberg JJ,

Zakrzewski VG, Dapprich S, Daniels AD, Strain MC, Farkas O, Malick DK, Rabuck AD,

Raghavachari K, Foresman JB, Ortiz JV, Cui Q, Baboul AG, Clifford S, Cioslowski J,

Stefanov BB, Liu G, Liashenko A, Piskorz P, Komaromi I, Martin RL, Fox DJ, Keith T,

Al-Laham MA, Peng CY, Nanayakkara A, Challacombe M, Gill PMW, Johnson B, Chen W, Wong MW, Gonzalez C, Pople JA (2004) Gaussian 03. Gaussian Inc, Wallingford CT 17. Dunning TH Jr, Hay PJ (1976) In: Schaefer III HF (ed) Modern Theoretical Chemistry,

Vol 3. Plenum, New York, pp 1-28

18. Hay PJ, Wadt WR (1985) J Chem Phys 82(1):270-283 19. Hay PJ, Wadt WR (1985) J Chem Phys 82(1):284-298 20. Hay PJ, Wadt WR (1985) J Chem Phys 82(1):299-310

21. Frisch MJ, Pople JA, Binkley JS (1984) J Chem Phys 80:3265-3269 22. Becke AD (1988) Phys Rev A 38:3098

23. Lee C, Yang W, Parr RG (1988) Phys Rev B 37:785 24. Becke AD (1993) J Chem Phys 98:5648-5652

25. Linstrom P, Mallard W (2003) NIST Chemistry WebBook, NIST Standard Reference Database Number 69. National Institute of Standards and Technology: Gaithersburg MD, p 20899. (http://webbook.nist.gov/)

26. Stewart JJP, http://openmopac.net/files.html

27. Cambridge Structural Database, Version 5.28 (2007) Cambridge Crystallographic Data Centre, Cambridge, UK

28. Clark T, Alex A, Beck B, Chandrasekhar J, Gedeck P, Horn AHC, Hutter M, Martin B, Rauhut G, Sauer W, Schindler T, Steinke T (2008) Computer-Chemie-Centrum, Universität Erlangen-Nürnberg: Erlangen

29. Stewart JJP (2002) LinMOPAC2.0. FQS Poland: Krakow

30. Stewart JJP (2007) MOPAC2007. Stewart Computational Chemistry, Colorado Springs, CO, USA. http://OpenMOPAC.net

31. Stewart JJP (2007) J Mol Model 13:1173-1213

Table 1

AM1* parameters for the elements Co and Ni

Parameter Co Ni

Uss [eV] -147.9969721 -47.9262400

Upp [eV] -75.4376929 -33.5123050

Udd [eV] -85.9948020 -92.9262050

_s [bohr^-1] 10.6559732 2.1694428

p [bohr^-1] 31.1355546 2.0212614

d [bohr^-1] 1.6662813 2.9999800

_s [eV] -94.1552039 -9.7800503

_p [eV] -126.5074725 -7.8215436

d [eV] -15.8120720 -10.1277693

gss [eV] 5.7855014 4.0808760

gpp [eV] 16.2498362 5.6217732

gsp [eV] 10.4339713 6.0176787

g_p2 [eV] 66.1182470 5.5014852

hsp [eV] 2.9132649 2.1328830

zsn [bohr^-1] 2.2158238 0.7464700

zpn [bohr^-1] 1.4599934 0.4533270

z_dn [bohr^-1] 1.4576614 1.4613450

(core) [bohr^-1] 1.6385615 1.3878582

H°_f(atom) [kcal mol^-1] 101.98 102.8

F⁰sd [eV] 7.9584630 4.6516640

G²_sd [eV] 6.6939630 1.8805020

(ij)

H 3.7250884 3.9112954

C 3.3514488 3.0416771

N 3.2268224 3.3195694

O 3.9648169 2.6648814

F 4.7295078 2.8884516

Al 2.2854320 2.4006390

Si 2.5793441 3.8488001

P 1.9571093 1.9182580

S 2.4315562 1.2619302

Cl 2.5666738 3.7009365

Ti 2.5672155 2.2550000

V 1.8037355 2.8635660

Cr 1.8441671 2.5326653

Co 2.9455643 3.5988970

Ni 3.5988970 2.3078430

Cu 2.0999846 2.4949800

Zn 2.5946347 2.9100500

Br 3.2938616 2.5296864

Zr 1.9076098 2.1815542

Mo 1.7152160 2.3116050

I 2.9718264 2.6608247

(ij)

H -7.4149924 -14.3720184

C 8.8159639 4.8355503

N 4.5514730 8.3058789

O 12.7561475 1.8194408

F 36.8730508 2.1280313

Al 3.6287393 4.4492610

Si 3.6071357 37.3623757

P 1.9376263 1.2970389

S 1.8108567 0.1685772

Cl 2.4236274 21.3405907

Ti 3.4060864 4.7044000

V 2.4096866 11.2551742

Cr 1.5174067 3.0903718

Co 18.3120000 35.4531600

Ni 35.4531600 2.4076920

Cu 0.8291495 3.5090000

Zn 1.3844244 4.1615000

Br 12.7590650 3.2087055

Zr 1.3523255 6.9245885

Mo 1.8055727 3.7298645

I 11.9594831 2.9999300

Table 2

Calculated AM1*, PM6 and PM5 heats of formation and errors compared with our target values for the cobalt-containing compounds used to parameterize AM1* (all values kcal mol

). Errors are classified by coloring the boxes in which they appear. Green indicates errors lower than 10 kcal mol

, yellow 10-20 kcal mol

and pink those greater than 20 kcal mol

. The codenames within parentheses indicate the CSD-names of the compounds

Compound

Target

H°f

AM1* PM6 PM5

H°f Error H°f Error H°f Error

Co^– 86.2 83.3 -2.9 -84.2 -170.4 43.8 -42.4

Co 102.0 102.0 0.0 82.3 -19.7 91.4 -10.6

Co⁺ 281.5 389.9 108.4 304.1 22.6 292.6 11.1

Co2 183.5 179.5 -4.0 -72.1 -255.6 114.5 -69.0

Co2–

137.6 146.8 9.2 -263.1 -400.7 121.1 -16.5

HCo 102.8 79.0 -23.8 50.5 -52.3 14.8 -87.9

HCo^– 98.5 67.6 -30.9 -52.0 -150.5 16.9 -81.6

C5H5Co^– 114.8 111.1 -3.7 10.0 -104.8 95.8 -19.0

CoC10H10 73.9 72.1 -1.8 52.4 -21.5 72.2 -1.7

CoCp2 (DCYPCO) 52.0 72.2 20.2 51.2 -0.8 71.4 19.4

CoC6N6H24

3+ (COTENC01) 587.5 587.8 0.3 557.2 -30.3 531.6 -55.9

CoC6N6H242+

(QICSOK) 280.9 263.3 -17.6 284.9 4.0 228.4 -52.5

CoC₉N₆H₁₅ (FEFRUD) 58.2 85.3 27.1 68.4 10.2 -24.8 -83.0

CoO^– 36.6 -38.9 -75.5 -130.2 -166.8 -81.4 -118.0

CoO2

– -34.0 -5.0 29.1 -57.7 -23.7 -109.1 -75.1

Co2(H2O)4

4+ 1052.6 1009.7 -42.8 857.5 -195.1 839.0 -213.5

Co(H2O)6

2+ 58.3 -51.7 -110.0 36.0 -22.3 -19.0 -77.3

Co(CO)4 -134.3 -153.2 -18.9 -136.8 -2.5 -62.5 71.8

CoH(CO)4 -136.0 -147.2 -11.2 -114.1 21.9 -152.2 -16.2

Co(CO)5+

4.1 -39.8 -43.9 33.4 29.3 38.2 34.1

CoC₆O₁₂^3– (Co(iii)(ox)₃) -542.2 -515.7 26.5 -532.3 9.9 -751.5 -209.3

Co2(CO)8 -283.0 -286.5 -3.5 -278.8 4.2 -253.6 29.4

CoN6H15O2

2+ (FAMYEX) 252.3 211.0 -41.3 247.2 -5.1 254.2 1.9

CoC6N4H16O4

+ (AETXCO) -93.9 -71.5 22.4 -68.0 25.9 -153.2 -59.3

CoC6N4H16O4

+ (OXENCO) -96.0 -77.7 18.3 -74.8 21.2 -159.3 -63.3

CoC6N6H18O4+

(NIXGEG) 27.9 26.3 -1.6 48.2 20.3 20.8 -7.1

CoC9N4H19O5 (AMGXCO01) -131.7 -92.4 39.3 -123.3 8.4 -158.5 -26.8

CoC6N6H20O6

+ (NITNCO) -39.2 -39.7 -0.5 -21.5 17.7 -123.3 -84.1

CoOF -70.8 -85.9 -15.1 -32.6 38.2 -128.8 -58.0

CoF2 -85.2 -85.2 0.0 -66.1 19.1 -85.4 -0.2

CoF3 -139.6 -180.7 -41.1 -137.1 2.5 -95.3 44.3

CoF4–

-302.0 -297.9 4.1 -253.8 48.2 -238.7 63.3

CoAlH2 125.9 92.4 -33.6 33.8 -92.1 49.7 -76.2

HCoAlH2 160.3 131.7 -28.6 80.3 -80.0 10.6 -149.7

CoSiH3 109.6 97.1 -12.5 32.2 -77.3 41.2 -68.4

CoP 131.2 131.3 0.0 79.3 -51.9 41.8 -89.5

CoPH2 100.3 72.5 -27.8 17.0 -83.3 -127.9 -228.2

HCoPH2 111.1 57.9 -53.2 38.6 -72.6 -68.1 -179.3

CoS 117.5 83.7 -33.8 20.8 -96.7 117.4 -0.1

CoSH 82.7 81.6 -1.1 4.7 -78.0 90.8 8.1

HCoSH 87.4 61.6 -25.8 4.9 -82.5 19.9 -67.4

CoC10H14S4 (TACACO10) -11.8 -1.9 9.9 -22.1 -10.3 -5.3 6.5

CoC9H21S6 (MEDTCO10) -65.7 -105.0 -39.3 -65.2 0.5 -72.6 -6.9

CoC3N3H6S6 (TDTCCO) -24.9 -25.1 -0.2 -7.1 17.8 30.9 55.8

CoCl 46.1 45.6 -0.5 51.6 5.5 35.3 -10.8

CoClO 13.8 7.9 -5.9 0.3 -13.5 -44.5 -58.3

CoCl2 -22.4 11.4 33.8 10.1 32.5 -38.8 -16.4

CoCl3 -39.1 -37.1 2.0 -24.5 14.6 -49.1 -10.0

Co2Cl4 -83.8 -81.4 2.4 -89.7 -5.9 63.5 147.3

CoC₄N₅H₁₉Cl²⁺ (ADETCO) 254.0 262.4 8.4 250.2 -3.8 224.5 -29.5

Co(NH3)2(H2O)2ClF⁺ -104.6 -147.8 -43.2 -113.3 -8.7 -128.2 -23.6

CoC2N4H8S2Cl2 (COTUCL11) -61.2 -54.2 7.0 -99.5 -38.3 -83.5 -22.3

CoC6N3H17Cl3 (AMPRCO) -159.2 -150.9 8.3 -138.4 20.8 -214.5 -55.3

CoC4N2H12SCl3 (CATBAA) -128.2 -118.7 9.5 -117.8 10.4 -159.5 -31.3

CoTi 116.0 116.0 0.0 66.4 -49.6 147.4 31.4

CoV 161.5 161.5 0.0 59.3 -102.2 -72.4 -233.9

CoCr 217.7 191.2 -26.5 89.3 -128.4 -347.4 -565.1

CoNi 108.1 108.2 0.1 1.4 -106.6 -118.0 -226.1

CoCu 143.1 141.8 -1.3 36.7 -106.4 -108.7 -251.9

HCoCu 150.9 150.9 0.0 79.2 -71.6 -127.7 -278.6

CoZn 124.6 114.3 -10.3 -158.1 -282.6 89.6 -34.9

HCoZn 121.4 91.7 -29.7 -78.0 -199.4 13.5 -107.9

CoBr 86.4 72.9 -13.5 61.0 -25.4 22.4 -64.0

CoOBr 19.9 -48.7 -68.6 17.6 -2.3 -129.4 -149.3

CoBr2 29.0 52.6 23.6 63.2 34.2 -94.6 -123.6

CoBr3 15.9 21.8 5.9 40.1 24.2 -149.5 -165.4

CoBr4 19.3 -10.6 -29.9 38.9 19.6 -196.7 -216.0

CoBr42–

-99.0 -100.3 -1.3 -169.9 -70.9 -286.5 -187.5

C4H8N4O5CoBr (BUKPIG) -99.6 -80.2 19.4 -121.0 -21.4 -152.7 -53.1

CoZr 209.8 172.1 -37.7 -10.4 -220.3 133.7 -76.2

CoMo 285.3 285.4 0.1 75.6 -209.6 288.2 3.0

HCoMo 280.4 261.9 -18.5 83.3 -197.1 222.7 -57.7

CoI 96.2 90.1 -6.2 49.9 -46.3 38.6 -57.6

ICoO 34.0 -2.7 -36.7 25.6 -8.4 -98.2 -132.2

CoI3 19.5 42.7 23.2 38.1 18.6 -78.0 -97.5

CoI4 39.0 40.0 0.9 -3.9 -42.9 -102.3 -141.3

C10H15NS2CoI (GECVEP) -13.3 38.7 52.0 2.5 15.8 -71.7 -58.4

C4H4N4O4CoI2

– (FIRCOY01) -16.8 -29.3 -12.5 -15.6 1.2 -135.0 -118.2

AM1* PM6 PM5

N=78

Most positive error 108.4 48.2 147.3

Most negative error -110.0 -400.7 -565.1

MSE -7.4 -48.6 -70.8

MUE 20.5 61.9 84.3

RMSD 30.4 98.1 121.8

Results for the PM6 parameterization set (N=42)

MSE -2.0 2.0 -32.4

MUE 22.9 15.7 52.5

RMSD 34.3 19.3 69.5

Table 3

Calculated AM1*, PM6 and PM5 Koopmans’ theorem ionization potentials and dipole moments for cobalt-containing compounds. The errors are color coded as follows: green up to 0.5 eV or 0.5 Debye; yellow between 0.5 and 1.0; pink larger than 1.0

Compound Target

AM1* PM6 PM5

Error Error Error

Koopmans' Theorem Ionization Potentials for Cobalt Compounds (eV)

CoCH3 7.00 8.88 1.88 9.57 2.57 9.01 2.01

CoC10H10 5.55 7.42 1.87 7.08 1.53 7.94 2.39

Co(CO)4 8.30 7.98 -0.32 8.97 0.67 8.04 -0.26

Co₂(CO)₈ 8.30 6.76 -1.54 10.86 2.56 8.78 0.48

CoCl 8.90 8.78 -0.12 9.48 0.58 8.29 -0.61

CoCl2 10.70 8.60 -2.10 8.27 -2.43 9.78 -0.92

CoBr2 9.90 9.09 -0.81 10.05 0.15 9.67 -0.23

AM1* PM6 PM5

N=7

MSE -0.16 0.80 0.41

MUE 1.23 1.50 0.99

Dipole Moments for Cobalt Compounds (Debye)

CoO^– 1.07 1.42 0.35 3.72 2.65 3.61 2.54

Co(CO)4 0.25 0.54 0.29 0.02 -0.23 4.35 4.10

CoH(CO)4 0.42 1.18 0.76 0.61 0.19 0.95 0.53

Co2(CO)8 1.23 1.23 0.00 0.23 -1.01 0.02 -1.21

CoOF 0.16 0.57 0.41 0.34 0.18 1.26 1.10

CoClO 0.93 1.31 0.38 0.81 -0.12 1.51 0.58

CoBr 3.65 1.88 -1.77 0.77 -2.88 5.67 2.02

CoBrO 1.81 1.98 0.17 3.44 1.63 1.33 -0.48

CoI 2.32 5.08 2.76 1.58 -0.74 5.91 3.59

CoIO 2.40 2.40 0.00 3.04 0.64 0.97 -1.43

AM1* PM6 PM5

N=10

MSE 0.34 0.03 1.13

MUE 0.69 1.03 1.76

Table 4

Calculated AM1*, PM6 and PM5 bond lengths and angles for cobalt-containing compounds. The codenames within parentheses indicate the CSD-names of the compounds. The errors are color coded as follows: green up to 0.05 Å or 0.5°; yellow between 0.05-0.1 Å or 0.5-1.0°; pink larger than 0.1 Å or 1°

Compound Variable Target

AM1* PM6 PM5

Error Error Error

Co2 Co-Co 2.30 2.45 0.15 2.07 -0.23 2.11 -0.19

Co2

– Co-Co 2.63 2.56 -0.08 2.10 -0.53 2.26 -0.37

HCo Co-H 1.55 1.59 0.04 1.71 0.16 1.40 -0.15

HCo^– Co-H 1.66 1.62 -0.04 2.20 0.54 1.44 -0.23

CoC₅H₅^– Co-C 1.93 2.00 0.07 2.07 0.14 2.27 0.34

Co(Cp2 (DCYPCO) Co-C 2.08 2.26 0.18 2.08 0.00 2.52 0.44

Co(CN)4

+ Co-C 1.81 2.00 0.19 1.77 -0.04 2.08 0.27

C-N 1.20 1.16 -0.04 1.16 -0.04 1.16 -0.04

Co(CN)6

3– Co-C 1.97 1.99 0.02 1.93 -0.04 2.16 0.19

CoC6N6H24 (Co(II)(en)3) Co-N 2.06 2.10 0.04 2.02 -0.04 2.21 0.15

CoC6N6H24

3+ (COTENC01) Co-N 2.00 2.00 0.00 2.01 0.01 2.21 0.21

N-Co-N 90.2 93.7 3.5 87.9 -2.3 81.4 -8.8

CoC₆N₆H₂₄²⁺ (QICSOK) Co-N 2.20 2.11 -0.09 2.24 0.04 2.26 0.06

N-Co-N 78.7 83.3 4.7 85.5 6.8 80.8 2.1

CoC9N6H15 (FEFRUD) Co-N 2.01 2.00 -0.01 2.06 0.05 2.23 0.22

N-Co-N 90.3 92.5 2.2 92.1 1.8 92.0 1.7

Co-C 1.89 2.05 0.16 1.84 -0.05 2.11 0.22

CoO^– Co=O 1.65 1.72 0.06 1.78 0.12 1.53 -0.13

CoO2

– Co=O 1.68 1.81 0.13 1.79 0.11 1.61 -0.07

Co(H2O)4

2+ Co-O 1.94 1.93 -0.02 1.91 -0.03 2.07 0.13

Co(H2O)6

3+ Co-O 2.03 1.94 -0.09 1.99 -0.04 1.99 -0.04

Co2(H2O)4

4+ Co-O 2.17 1.96 -0.21 1.92 -0.25 1.95 -0.22

Co(H2O)6

2+ (NAZVOZ) Co-O 2.06 1.97 -0.09 1.88 -0.18 1.52 -0.54

Co-O' 2.12 2.02 -0.10 1.87 -0.25 2.23 0.11

Co(H2O)6

2+ Co-O 2.12 1.96 -0.16 1.99 -0.13 2.11 -0.02

Co-O' 1.96 1.95 -0.01 2.01 0.05 2.09 0.13

Co(CO)4 Co-C 1.85 1.89 0.04 1.98 0.13 2.18 0.33

Co(CO)4–

(FUBYOQ) Co-C 1.75 1.95 0.20 1.90 0.15 2.04 0.29

CoH(CO)4 Co-H 1.55 1.62 0.06 1.70 0.14 1.39 -0.17

Co-C 1.81 1.90 0.09 1.83 0.02 2.02 0.21

Co(CO)5

+ Co-C(eq) 1.83 2.00 0.17 1.82 -0.01 2.07 0.24

Co-C(ax) 1.89 1.92 0.03 1.82 -0.07 2.92 1.03

CoC6O12

3– (Co(iii)(ox)3) Co-O 1.95 1.95 0.00 1.98 0.03 2.00 0.05

Co2(CO)8 Co-Co 2.47 3.08 0.61 2.47 0.00 3.50 1.03

Co(CO)3NO Co-C 1.81 1.94 0.13 2.14 0.33 2.04 0.23

C-Co-C 103.2 85.9 -17.3 81.0 -22.2 93.1 -10.2

Co-N 1.67 1.74 0.07 1.60 -0.07 1.93 0.26

Co(NO3)3 Co-O 1.89 1.84 -0.05 1.88 -0.01 2.19 0.30

O-Co-O 68.0 65.3 -2.7 71.1 3.1 176.0 108.0

O-Co-O' 93.0 98.8 5.8 98.6 5.6 86.8 -6.2

CoN6H15O2

2+ (FAMYEX) Co-N(O2) 1.95 1.91 -0.04 1.79 -0.16 2.09 0.14

Co-N(H3) 1.96 2.08 0.12 2.03 0.07 2.20 0.24

N-Co-N 90.0 92.9 2.9 89.0 -1.0 88.8 -1.2

CoC6N4H16O4+

(OXENCO) Co-N 1.98 2.04 0.06 1.98 0.00 2.30 0.32

N-Co-N 86.0 85.3 -0.7 89.7 3.6 81.2 -4.8

Co-O 1.94 1.92 -0.02 1.95 0.01 1.91 -0.03

CoC6N4H16O4

+ (AETXCO) Co-O 1.92 1.90 -0.02 1.93 0.01 1.91 -0.01

O-Co-O 84.8 84.3 -0.5 87.8 3.0 85.9 1.1

Co-N(H2C) 1.98 2.05 0.07 1.96 -0.02 2.21 0.23

Co-N(H3) 1.95 2.04 0.09 2.00 0.05 2.27 0.32

C-N(HC2) 1.92 2.07 0.15 1.94 0.02 2.23 0.31

CoC₆N₆H₁₈O₄⁺ (NIXGEG) Co-N(C3) 1.96 2.11 0.15 1.96 0.00 2.20 0.24

Co-N(CH2) 1.96 2.09 0.13 2.04 0.08 2.20 0.24

N-Co-N 86.8 87.7 0.9 85.4 -1.4 90.7 3.9

Co-N(O2) 1.99 2.01 0.02 1.87 -0.12 2.13 0.14

Co-N(O2) 1.93 1.90 -0.03 1.83 -0.10 2.08 0.15

CoC9N4H19O5 (AMGXCO01) Co-N 1.89 1.99 0.10 1.88 -0.01 2.12 0.23

N-Co-N 82.0 82.1 0.1 82.8 0.8 74.5 -7.5

Co-C 1.98 2.04 0.06 2.01 0.03 2.15 0.17

Co-O 2.06 2.03 -0.03 2.21 0.15 2.16 0.10

CoC15H21O6

– (Co(II)(Acac)3(-) IKEYAY) Co-O 2.06 1.95 -0.11 2.12 0.06 1.97 -0.09

O-Co-O 88.0 87.0 -0.9 101.1 13.1 94.0 6.1